Activities to Practice Multiplication and Division-One of the best ways to work on computational fluency is through problem solving. Cognitively Guided Instruction has identified several different problem structures for multiplication and division. Please see article about Cognitively Guided Instruction for a listing of these problem structures. In addition to solving problems, students should also participate in activities that will foster their fluency with multiplying and dividing numbers. Many students feel overwhelmed when they are trying to become automatic with the basic facts. To help them feel more confident in this process it is helpful to make a systematic plan for learning the facts based on the factors.
One of the biggest things for students to realize is that turn-around facts are equal to each other. For instance, 4 * 6 = 6 * 4. This is known as the commutative property. The goal is for students to display fluency by the quick (3 seconds or less) and accurate recall of facts without resorting to counting strategies. Utilizing related strategies such as doubles, double doubles (4 facts), and triple doubles (8 facts) are strategies to get kids to see relationships rather than resorting to guessing or counting strategies. With enough repetition the fact 6*8 solved as 6*(2*2*2) will be memorized as 6*8 = 48.
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Activities that work all the facts: These activities can be used to work the basic facts or multi-digit computation. The Open Array is a very useful tool as students transition from using manipulatives to count out the answer to solving either mentally or using a paper and pencil procedure. Circles and Stars This game is played with three people, a caller and two players. This game can be played with dice (to practice the facts 1 – 6) or a deck of cards (to practice the facts 1 – 10). The caller rolls the dice or flips over two cards. They call out the multiplication sentence. Players can either call the fact if they know it or try the graphic to figure it out. The graphic is to draw a circle for the first factor (one dice or one card) and the number of stars in each circle is the other factor (the other dice or card). Students still learning their fact may need to draw the graphic and skip count to figure out the product. With practice they should be able to recall the facts quickly and accurately without the graphic. For instance, if the fact was 3 * 5 = The graphic would look like this:
Play until one player has correctly answered ten facts. The winner becomes the caller and the other two players play again.
Rows and Columns This game is very similar to Circles and Stars, but the graphic is different. In this game players use graph paper to create an array based on the number sentence. The first factor tells them how many rows to make, the second factor tells them how many columns to make.
For instance, if the number sentence was 4 * 5 =
The graphic would have 4 rows and 5 columns.
Here is another way to show the same thing.
Students can figure out the product by counting boxes, skip counting rows or columns or simply recalling that 4 * 5 = 20. Play until one player has correctly answered ten facts. The winner becomes the caller and the other two players play again.
Mathematical War
Materials: Deck of cards Number of players: 2 Object: To win the most “battles” and have the biggest “army”.
Directions: A battle begins with both players flipping over a card at the same time. The player that calls out the sum, difference, or product correctly first wins the battle and takes both cards. Play for a set amount of time, player with the most cards at the end of the time has the biggest army and wins the game.
This game can be played to practice addition, subtraction, and multiplication facts. Face cards (King, Queen, Jack) are read as 10. Example 3 * K is read as 3 * 10. Ace is read as 1.
Players can remove cards from the deck if they want to practice certain facts.
How Many? How Many Circles? How many in Each? Materials: Counters, paper and pencil, dice or spinner optional (to determine number of circles). Objective: This is an individual game to practice the division concept. Student takes a handful of counters (anything will work, candy, cereal, coins, etc). Can have them estimate how many and then check if you want, but this is not required. Student then decides how many circles to draw. They sort the counters into the circles so that they have equal groups. Students then write the division sentence to match the action. How many objects ÷ Number of circles = number of objects in each circle. Note students will have to deal with remainders so they need to know how to record these in the case that the counters do not sort evenly.
Can modify this game to work on the rectangular array model by having students ask How many? How many Rows? How many Columns? They play the same way, but instead of choosing the number of circles they choose the number of rows and then arrange the counters into equal rows until all counters that can be used are placed and then they record the matching division sentence. How many objects ÷ Number of Rows = Number of Columns.
Living Fact Triangles Or Mathematical War – Division Practice Materials: Deck of cards Number of players: 3 Object: To win the most “battles” and have the biggest “army”.
Directions: Players sit in a triangle. Two players divide up the cards. The third player has no cards because they are the caller. A battle begins with two players putting a card on their forehead without looking at it. They can see the other player’s card, but not their own. The caller mentally solves the problem and announces the product. Players figure out what is on their head based on the product and the factor they can see. Example: Caller: “The product is 40.” Player 1 sees the card “5” on the other players forehead. They think, “What times 5 equals 40?” or “40 divided by what equals 5?” At the same time Player 2 sees the card “8” and they are thinking in the same way, just with the other equations in the fact family. (“What times 8 equals 40?” or “40 divided by what equals 8?”) The player who figures out what is on their forehead first wins both cards.
Play for a set amount of time, player with the most cards at the end of the time has the biggest army and wins the game. Face cards (King, Queen, Jack) are read as 10. Example 3 * K is read as 3 * 10. Ace is read as 1. Players can remove cards from the deck if they want to practice certain facts.
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